Probability tree.

[bmcthankies]

Hi, first post here! I’m stuck on this question:/. My teacher hasn’t given any lecture about this subject, so I’m kinda bad at it. I’ll translate the homework since it’s in another language:

Suzan has created the following game: The computer generates a random integer from 100 to 999. The number is only visible to the game leader. The player has one attempt to guess the number. If the number is guessed correctly, the player receives €500. If two numbers are guessed in the correct place, the player receives €10. Guessing one number correctly of the three results in a prize of €1.

Questions:
-Draw a probability tree for this game
-Explain the chance of the payout of €10 is almost 3%
-Give the probability distribution of the payout.
-Calculate the minimum stake that Suzan must ask per game to make a profit in the long run.

Sorry for the long post!!

 

[mmm4444bot]

I’m stuck on this question. My teacher hasn’t given any lecture about this subject

Hello. Are you saying that this is the first time you've seen the name 'probability tree'? Since your teacher has not mentioned it, is there any information in your textbook? If not, have you tried searching for online lectures or written material? We don't provide lectures here.

Sorry for the long post!

No need for apologizing. You don't have any control over the length of exercise statements.

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[bmcthankies]

Hello. Are you saying that this is the first time you've seen the name 'probability tree'? Since your teacher has not mentioned it, is there any information in your textbook? If not, have you tried searching for online lectures or written material? We don't provide lectures here.


No need for apologizing. You don't have any control over the length of exercise statements.

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...

www.freemathhelp.com

Hey! No, I know what probability trees are, but I can’t seem to figure out how to create them. Questions like these have me stumped and I’ve watched a couple of videos and have read my books a couple of times now.

 

[BigBeachBanana]

Here's the first result I found from a search from mathisfun.com. This is the classic example of tossing a fair coin. Looking at this tree, what don't you understand?

 

[bmcthankies]

Here's the first result I found from a search from mathisfun.com. This is the classic example of tossing a fair coin. Looking at this tree, what don't you understand?
View attachment 38308

Thank you for your reply! This example is pretty clear, but I can’t really apply it to other situations. For example, the question in my original post. I don’t really know how many branches I should draw, what nodes, and where I should put what.

 

[mmm4444bot]

I know what probability trees are, but I can’t seem to figure out how to create them.

We need to know why. Is it the calculation of the probabilities? It is the counting of possibilitites? Something else?

If two numbers are guessed in the correct place, the player receives €10. Guessing one number correctly of the three results in a prize of €1.

FYI: In English, we would say "digits" and "digit" above.

Also, do you interpret the last sentence above to mean correctly guessing one digit in the correct position?
[imath]\;[/imath]

 

[bmcthankies]

We need to know why. Is it the calculation of the probabilities? It is the counting of possibilitites? Something else?


FYI: In English, we would say "digits" and "digit" above.

Also, do you interpret the last sentence above to mean correctly guessing one digit in the correct position?
[imath]\;[/imath]

Hi! Yeah digits, my bad! so guessing digits in the correct position it is. And I’m struggling with both, calculating the possibilities and the counting of possibilities

 

[BigBeachBanana]

Hi! Yeah digits, my bad! so guessing digits in the correct position it is. And I’m struggling with both, calculating the possibilities and the counting of possibilities

Are you guessing from right to left or left to right? It makes a difference when drawing the tree as you don't have 0 as an option for the left-most digit.

 

[bmcthankies]

Are you guessing from right to left or left to right? It makes a difference when drawing the tree as you don't have 0 as an option for the left-most digit.

I’ve been guessing from right to left. Is that wrong?

 

[BigBeachBanana]

I’ve been guessing from right to left. Is that wrong?

I said "different" not wrong.
What do you think, for the tree, should be the first split and their probabilities?

 

[bmcthankies]

I said "different" not wrong.
What do you think, for the tree, should be the first split and their probabilities

Well, I’ve made a quick sketch. A being €500, B being €10 and C being €1. Think I’m not taking the right steps

 

[Dr.Peterson]

Hi, first post here! I’m stuck on this question:/. My teacher hasn’t given any lecture about this subject, so I’m kinda bad at it. I’ll translate the homework since it’s in another language:

Suzan has created the following game: The computer generates a random integer from 100 to 999. The number is only visible to the game leader. The player has one attempt to guess the number. If the number is guessed correctly, the player receives €500. If two numbers are guessed in the correct place, the player receives €10. Guessing one number correctly of the three results in a prize of €1.

Questions:
-Draw a probability tree for this game
-Explain the chance of the payout of €10 is almost 3%
-Give the probability distribution of the payout.
-Calculate the minimum stake that Suzan must ask per game to make a profit in the long run.

First, let's retranslate the problem using what has been discussed so far:

Suzan has created the following game: The computer generates a random integer from 100 to 999. The number is only visible to the game leader. The player has one attempt to guess the number. If the (entire) number is guessed correctly, the player receives €500. If two digits are guessed in the correct place, the player receives €10. Guessing one digit correctly of the three (in the correct place) results in a prize of €1.​

​

Questions:​

• Draw a probability tree for this game
• Explain the chance of the payout of €10 is almost 3%
• Give the probability distribution of the payout.
• Calculate the minimum stake that Suzan must ask per game to make a profit in the long run.

The trouble I have is that you are not guessing one digit at a time, so a tree like the coin tossing example, where the tree is used to find the probabilities, isn't quite appropriate. Yours is closer; but I think it would be just as reasonable to make a tree consisting merely of three branches -- no, make that four:

• All three digits correct
• Exactly two digits correct
• Exactly one digit correct
• No digits correct

Now you just need to find the probability of each of these. Probably the first and last are easiest; can you show us what you find for those? You won't be using the tree to do this. But it will help if you can show the steps you take, so we can have a better idea of what you have learned.

(Your probability for A is almost right, but not quite.)

For the middle two cases, we'll want to see how you have been taught to find probabilities of this sort, so even a "failed" attempt will show us something.

Incidentally, it might be helpful if you could show an example or two from your textbook (it's okay that it's not in English), showing how they make a tree, and what sort of application they use it for. (There are different styles for different purposes.) Also, when you say there has been no lecture on this subject, do you mean you have been taught nothing on probability, or just on trees, or on games and expected value and so on.

 

[bmcthankies]

First, let's retranslate the problem using what has been discussed so far:

Suzan has created the following game: The computer generates a random integer from 100 to 999. The number is only visible to the game leader. The player has one attempt to guess the number. If the (entire) number is guessed correctly, the player receives €500. If two digits are guessed in the correct place, the player receives €10. Guessing one digit correctly of the three (in the correct place) results in a prize of €1.​

​

Questions:​

• Draw a probability tree for this game
• Explain the chance of the payout of €10 is almost 3%
• Give the probability distribution of the payout.
• Calculate the minimum stake that Suzan must ask per game to make a profit in the long run.

The trouble I have is that you are not guessing one digit at a time, so a tree like the coin tossing example, where the tree is used to find the probabilities, isn't quite appropriate. Yours is closer; but I think it would be just as reasonable to make a tree consisting merely of three branches -- no, make that four:

• All three digits correct
• Exactly two digits correct
• Exactly one digit correct
• No digits correct

Now you just need to find the probability of each of these. Probably the first and last are easiest; can you show us what you find for those? You won't be using the tree to do this. But it will help if you can show the steps you take, so we can have a better idea of what you have learned.

(Your probability for A is almost right, but not quite.)

For the middle two cases, we'll want to see how you have been taught to find probabilities of this sort, so even a "failed" attempt will show us something.

Incidentally, it might be helpful if you could show an example or two from your textbook (it's okay that it's not in English), showing how they make a tree, and what sort of application they use it for. (There are different styles for different purposes.) Also, when you say there has been no lecture on this subject, do you mean you have been taught nothing on probability, or just on trees, or on games and expected value and so on.

I haven’t really been taught anything about probability or trees and have asked my teacher many times for help but sadly I didn’t receive any. The book isn’t the best in my opinion as the theory they give is very much a shortened simple version. Here is an example of my book.

And how can I find the probability? Sorry if I’m asking too many questions! It’s just that my teacher won’t help me with my questions and videos don’t seem to cut it:/

 

[Harry_the_cat]

I would draw it like the heads/tails example. But label the first 2 branches as "first digit correct" and "first digit incorrect". The the branches coming off each of these as "second digit correct" and "second digit incorrect" . Then same for the third. Label the branches with the appropriate probabilites.

 

[BigBeachBanana]

What I had in mind was a little different for the tree.
Edit: What Harry_the_cat said.

 

[Dr.Peterson]

Here is an example of my book.

Given that this is all you have been taught, what the others suggest is probably what you need to do.

In addition to labeling probabilities, label each end point with the number of correct digits, and therefore with the value.

 

[bmcthankies]

What I had in mind was a little different for the tree.
Edit: What Harry_the_cat said.

View attachment 38313

Sorry for the late reply! but thank you so much for your help. Sadly I didn’t get a good grade for the test, but that’s okay! I’ll just work harder to understand it more

 

[bmcthankies]

Given that this is all you have been taught, what the others suggest is probably what you need to do.

In addition to labeling probabilities, label each end point with the number of correct digits, and therefore with the value.

Thank you!

 

[BigBeachBanana]

I’ll just work harder to understand it more

As part of your working-harder goal, you should finish the problem.